Question
Find the polynomial having roots at $ 2 $ , $ 10 $ , $ 60 $ , $ 420 $ and $ 42 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^5-534x^4+51644x^3-1613160x^2+13608000x-21168000 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 2 $ | $ x-2 $ |
| $ 10 $ | $ x-10 $ |
| $ 60 $ | $ x-60 $ |
| $ 420 $ | $ x-420 $ |
| $ 42 $ | $ x-42 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x-10 \right) \cdot \left( x-60 \right) \cdot \left( x-420 \right) \cdot \left( x-42 \right) = x^5-534x^4+51644x^3-1613160x^2+13608000x-21168000 $$This page was created using
Polynomial From Roots Calculator